The government already does this by subsidizing low income earners via the EITC. It just outsources the actual job provision to the private sector, which is an effective alternative to wasteful make-work.
Except that doesn’t work as there remains a systemic shortage of jobs on offer.
The societal deal with the private sector is that it employs everybody at a rate that allows an individual to live in return for the chance to make a profit. A job guarantee ensures that the private sector overall cannot shirk that responsibility.
If the private sector does its job, nobody will be employed on a job guarantee.
An income subsidy does the same thing at lesser cost. Whether that subsidy is a UBI or a wage supplement is to some extent a political choice: we got the EITC instead of a proper UBI (managed as a "negative" income tax bill for low-earning folks) largely due to political objections to the notion of getting money "for doing nothing".
Yet the state pension tells us that isn’t the case. The state pension is a UBI allocated by age rather than physical area. We have millions of data points showing that when people receive sufficient to live on they stop working.
The result is political pressure to remove the state pension or increase the age at which it is received.
If UBI worked as you suggest then the resulting increase in productivity would drive the state pension age down not up.
The evidence is against you. Giving people money reduces productivity and makes it more difficult for firms to get the labour they require, and at huge cost to the state that uses up the finite taxation space there is available.
